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Question
If A = {1, 2, 3, 4 }, define relations on A which have properties of being:
symmetric but neither reflexive nor transitive
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Solution
Given that, A = {1, 2, 3}.
Let R2 = {(1, 2), (2, 1)}
Now, (1, 2) ∈ R2, (2, 1) ∈ R2
So, it is symmetric,
And, clearly R2 is not reflexive as (1, 1) ∉ R2
Also, R2 is not transitive as (1, 2) ∈ R2, (2, 1) ∈ R2 but (1, 1) ∉ R2
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